THE STRUCTURED CONDITION NUMBER OF A DIFFERENTIABLE MAP BETWEEN MATRIX MANIFOLDS, WITH APPLICATIONS

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dc.authorid0000-0002-7750-4325en_US
dc.contributor.authorArslan, Bahar
dc.contributor.authorNoferini, Vanni
dc.contributor.authorTisseur, Francoise
dc.date.accessioned2021-03-20T20:12:51Z
dc.date.available2021-03-20T20:12:51Z
dc.date.issued2019
dc.departmentBTÜ, Mühendislik ve Doğa Bilimleri Fakültesi, Matematik Bölümüen_US
dc.descriptionNoferini, Vanni/0000-0002-1775-041X; Tisseur, Francoise/0000-0002-1011-2570en_US
dc.description.abstractWe study the structured condition number of differentiable maps between smooth matrix manifolds, extending previous results to maps that are only R-differentiable for complex manifolds. We present algorithms to compute the structured condition number. As special cases of smooth manifolds, we analyze automorphism groups, and Lie and Jordan algebras associated with a scalar product. For such manifolds, we derive a lower bound on the structured condition number that is cheaper to compute than the structured condition number. We provide numerical comparisons between the structured and unstructured condition numbers for the principal matrix logarithm and principal matrix square root of matrices in automorphism groups as well as for the map between matrices in automorphism groups and their polar decomposition. We show that our lower bound can be used as a good estimate for the structured condition number when the matrix argument is well conditioned. We show that the structured and unstructured condition numbers can differ by many orders of magnitude, thus motivating the development of algorithms preserving structure.en_US
dc.description.sponsorshipRepublic of Turkey Ministry of National EducationMinistry of National Education - Turkey; European Research Council Advanced grant MATFUN [267526]; Engineering and Physical Sciences Research CouncilUK Research & Innovation (UKRI)Engineering & Physical Sciences Research Council (EPSRC) [EP/I005293]; Royal Society-Wolfson Research Merit AwardRoyal Society of Londonen_US
dc.description.sponsorshipThe first author's research was supported by the Republic of Turkey Ministry of National Education. The second author's work was partially supported by European Research Council Advanced grant MATFUN (267526). The third author's research was supported by Engineering and Physical Sciences Research Council grant EP/I005293 and by a Royal Society-Wolfson Research Merit Award.en_US
dc.identifier.doi10.1137/17M1148943en_US
dc.identifier.endpage799en_US
dc.identifier.issn0895-4798
dc.identifier.issn1095-7162
dc.identifier.issue2en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage774en_US
dc.identifier.urihttp://doi.org/10.1137/17M1148943
dc.identifier.urihttps://hdl.handle.net/20.500.12885/719
dc.identifier.volume40en_US
dc.identifier.wosWOS:000473026800016en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.institutionauthorArslan, Bahar
dc.language.isoenen_US
dc.publisherSiam Publicationsen_US
dc.relation.ispartofSiam Journal On Matrix Analysis And Applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectmatrix functionen_US
dc.subjectFrechet derivativeen_US
dc.subjectcondition numberen_US
dc.subjectbilinear formen_US
dc.subjectsesquilinear formen_US
dc.subjectstructured matricesen_US
dc.subjectstructured condition numberen_US
dc.subjectautomorphism groupen_US
dc.subjectLie algebraen_US
dc.subjectJordan algebraen_US
dc.subjectpolar decompositionen_US
dc.titleTHE STRUCTURED CONDITION NUMBER OF A DIFFERENTIABLE MAP BETWEEN MATRIX MANIFOLDS, WITH APPLICATIONSen_US
dc.typeArticleen_US

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